# Rapiers for Fighters Light or One Handed Weapon?

Background:

I'm trying to build a TWF Fighter who focuses on criticals. I was looking for a weapon that would let me leverage power attack and still let me dual wield so proficiency would apply to both and is 18/20.

I came across the rapier which seems to fit the bill nicely. So nicely, that I'm trying to understand if this is a mistake:

One-Handed Melee Weapons:

Rapier |    20 gp | 1d4  | 1d6   | 18–20/×2 —   | 2 lbs.    | P | —


But if I look at the fighter's groups under weapons training:

 Blades, Light: dagger, kama, kukri, **rapier**, sickle, starknife, and short sword.


Question:
What I'm seeing is that I can use the same weapon to power attack with as I can use to twf and only take the -2/-2 penalty. Is that correct?